Neighborhood of a Point definition of Neighborhood of a Point in the Free Online Encyclopedia.

neighborhood of a point [′nā·bər‚hu̇d əv ə ′pȯint]

(mathematics)

A set in a topological space which contains an open set which contains the point; in Euclidean space, an example of a neighborhood of a point is an open (without boundary) ball centered at that point.

Neighborhood of a Point

(for a metric space), the set of all points whose distance from a given point is less than some positive number R. A neighborhood of this type is called spherical, and the number R is called the radius of the neighborhood. Also frequently considered are rectangular neighborhoods in a plane and their analogs in spaces of any number of dimensions. Sometimes the neighborhood of a point on a line is understood to mean any interval that includes this point, and the neighborhood of a point on a plane is understood to mean any open circle that includes this point but, perhaps, does not have the point as a center. These and other special types of neighborhoods are special cases of more general neighborhoods that are understood to mean all open sets that contain the given point.

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Neighborhood Impact Coordinating Committee
Neighborhood Improvement District Management Association
Neighborhood Improvement Foundation of Toledo, Inc.
Neighborhood Improvement Program
Neighborhood Improvement Strategy
Neighborhood Institute for the Arts
Neighborhood Integrated Service Team
Neighborhood Jobs Initiative
Neighborhood Justice Center
Neighborhood Knowledge Los Angeles
Neighborhood Learning Center Network
Neighborhood Legal Clinic
Neighborhood Legal Services Association
Neighborhood Legal Services Michigan
Neighborhood Legal Services Program
Neighborhood Lending Partners of West Florida
Neighborhood Lending Services
Neighborhood Liaison Working Group
Neighborhood List Interference Loading
Neighborhood Main Street Initiative
Neighborhood Network in Palliative Care
Neighborhood Networks Center
Neighborhood Nonprofit Housing Corporation
Neighborhood Nuclear Superiority

Neighborhood of a Point

Neighborhood of the Arts
Neighborhood of the Year
Neighborhood Open Space Coalition
Neighborhood Oriented Policing
Neighborhood Ownership Recovery Mortgage Assistance Loan
Neighborhood Parks Council
Neighborhood Partnership Housing Services, Inc
Neighborhood Pattern Sensitive Fault
Neighborhood Physical Activity Questionnaire
Neighborhood Planning Action Committee
Neighborhood Planning and Zoning Department
Neighborhood Planning for Community Revitalization
Neighborhood planning unit
Neighborhood Policing
Neighborhood Policing Teams
Neighborhood Preservation Homeowner Exemption
Neighborhood Preservation Zone
Neighborhood Processor
Neighborhood Proportional Delay Differentiation
Neighborhood Public Radio
Neighborhood Quality of Life Study
Neighborhood Random Early Detection
Neighborhood Reinvestment Corporation
Neighborhood Reinvestment Training Institute